The short answer is yes .. this is a longer post, so please read on
NYT on Reinfection
Bloomberg on Reinfection https://www.bloomberg.com/news/articles/2020-04-14/do-coronavirus-survivors-have-immunity-from-reinfection-maybe
First a primer on immune systems ... we have in effect, many different and independent immune responses that all weave themselves together into an "immune system" ... Aside from natural barriers (skin, stomach acid, nasal hair, etc...), an incomplete and high level list of main categories: fast acting responders (typically non-specific), long acting responders (memory cells and specific antibodies), phagocytes, lymphocytes
Very simplistically, the short and long acting responders bind to foreign viral and bacterial invaders ... once bound, they signal to phagocytes and lymphocytes to eat whatever they're attached to ... The phagocytes eat anything they don't recognize, and sometimes they recognize things as foreign without the assistance of antibodies ... when I spoke of "Cytokine Storms" earlier in this blog, what I'm talking about is a situation where the phagocytes go haywire and start killing everything - eventually leading to ARDS, kidney failure, cardiac issues and death ... there are approved and experimental drugs that can quell this over response which are being studied as therapeutics for that specific situation, but these are not *cures* for CoVID-19 - just treatments ("therapeutics")
Back to the "responders" ... these are typically antibodies (there are many different kinds - IgG, IgM, IgA, IgD, IgE) and they need a *SPECIFIC* genetic target to recognize and attach to ... if this target stays the same, the next time the body encounters the invader, it typically easily disposes of the infection ... this is how vaccines work but it presumes the target stays the same ... if the target changes (as can occur in a new strain), then the antibody doesn't recognize the invader as "foreign" and you're no longer "immune"
SARS-CoV-2 accumulates about 3-4 easily identifiable mutations per month ... this slow rate of mutation is good news - it means that its likely that the immune response to an early infection will remain protective ... however, given that there is already documentation of *recovereds getting sick again*, it means that the virus is mutating in ways that change the targets the antibody responders recognize ... this is not a disaster, but makes vaccine development more complicated - you don't want to develop a vaccine that needs to be readministered yearly for a virus like this (a'la influenza) ... we will want a vaccine that confers a multiyear or permanent immunity (like polio) ... this means we need to identify a target on the surface of the virus, accessible to the immune responders that stays the same through all strains - it seems like we're much of the way there
In the short term, recovereds are prolly safe from getting reinfected within the "season" and within a geography since the endemic virus is prolly going to be the same in a geo area for a few months at a stretch
There are also reports of about 10% of recovereds not having detectable antibodies to SARS-CoV-2 ... whether this is a false negative result, or in fact some other component of the immune system cleared the virus is unclear and needs further study .. if in fact, these folks do not have antibodies, they are *not* immune even though they have recovered from one bout of infection https://en.yna.co.kr/view/AEN20200406006700320